featured book

featured book

Journey through Genius

The Great Theorems of Mathematics

Format

Paperback

Price

$17.00

Paperback

ISBN 9780140147391

320 Pages

1 Aug 1991

Penguin Books

18 and up

Overview

Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.

Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.

A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

Journey through Genius

Praise

“It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” — Isaac Asimov

“Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.”—Ivars Peterson, author of The Mathematical Tourist

Table of Contents

Journey through Genius – William Dunham PrefaceAcknowledgmentsChapter 1. Hippocrates’ Quadrature of the Lune (ca. 440 B.C.)The Appearance of Demonstrative MathematicsSome Remarks on QuadratureGreat TheoremEpilogueChapter 2. Euclid’s Proof of the Pythagorean Theorem (ca. 300 B.C.)The Elements of EuclidBook I: PreliminariesBook I: The Early PropositionsBook I: Parallelism and Related TopicsGreat TheoremEpilogueChapter 3. Euclid and the Infinitude of Primes (ca. 300 B.C.)The Elements, Books II-VINumber Theory in EuclidGreat TheoremThe Final Books of the ElementsEpilogueChapter 4. Archimedes’ Determination of Circular Area (ca. 225 B.C.)The Life of ArchimedesGreat TheoremArchimedes’ Masterpiece: On the Sphere and the CylinderEpilogueChapter 5. Heron’s Formula for Triangular Area (ca. A.D. 75)Classical Mathematics after ArchimedesGreat TheoremEpilogueChapter 6. Cardano and the Solution of the Cubic (1545)A Horatio Algebra StoryGreat TheoremFurther Topics on Solving EquationsEpilogueChapter 7. A Gem from Isaac Newton (Late 1660s)Mathematics of the Heroic CenturyA Mind UnleashedNewton’s Binomial TheoremGreat TheoremEpilogueChapter 8. The Bernoullis and the Harmonic Series (1689)The Contributions of LeibnizThe Brothers BernoulliGreat TheoremThe Challenge of the BrachistochroneEpilogueChapter 9. The Extraordinary Sums of Leonhard Euler (1734)The Master of All Mathematical TradesGreat TheoremEpilogueChapter 10. A Sampler of Euler’s Number Theory (1736)The Legacy of FermatGreat TheoremEpilogueChapter 11. The Non-Denumerability of the Continuum (1874)Mathematics of the Nineteenth CenturyCantor and the Challenge of the InfiniteGreat TheoremEpilogueChapter 12. Cantor and the Transfinite Realm (1891)The Nature of Infinite CardinalsGreat TheoremEpilogueAfterwordChapter NotesReferencesIndex